Non-demolition tomography of quantum states in a mechanical oscillator*

Nanomechanical oscillators display many useful properties for technological applications, motivating their integration into the domain of quantum information science. In the field of quantum acoustics, one important effort is to leverage the strong nonlinearity and established control techniques of superconducting qubits to prepare and characterize quantum states of motion in mechanical oscillators. Studies of nonclassical mechanical states have been conducted in recent experiments using surface acoustic waves [1] and bulk acoustic waves [2] through a resonant qubit-mechanics interaction. In this talk, we present a quantum non-demolition approach to performing Wigner tomography on a mechanical oscillator, which leverages strong dispersive coupling between a superconducting transmon qubit and a thin-film phononic crystal resonator. We use the qubit to prepare quantum states of phonons in the resonator, and perform full quantum state tomography on the mechanical mode through a Ramsey measurement. We present experimental results and show that our measured state fidelities are in good agreement with numerical models that include energy dissipation in the mechanical oscillator.

[1] K. J. Satzinger et al, Nature 563, 661–665 (2018)

[2] Y. Chu et al, Nature 563, 666–670 (2018)